Dynamical phenomena connected with stability loss of equilibria and periodic trajectories

This is a study of a dynamical system depending on a parameter . Under the assumption that the system has a family of equilibrium positions or periodic trajectories smoothly depending on , the focus is on details of stability loss through various bifurcations (Poincaré–Andronov– Hopf, period-doubling, and so on). Two basic formulations of the problem are considered. In the first, is constant and the subject of the analysis is the phenomenon of a soft or hard loss of stability. In the second, varies slowly with time (the case of a dynamic bifurcation). In the simplest situation , where is a small parameter. More generally, may be a solution of a slow differential equation. In the case of a dynamic bifurcation the analysis is mainly focused around the phenomenon of stability loss delay. Bibliography: 88 titles.

Dynamic bifurcation analysis and mitigation of SSR in SMIB system

This paper presents a detailed study on Sub-synchronous resonance in a Single machine connected to an infinite bus system by employing Bifurcation Theory. The synchronous machine model considered is a two-axis model, the turbine system is a six mass system. A comparative study of Sub-synchronous resonance for the two-axis synchronous machine models 1.1, 2.1 and 2.2 under constant excitation is presented in this paper. The effect of adding an exciter, power system stabilizer and Static Synchronous Series Compensator to the SMIB system, incorporated with a 2.2 synchronous machine model on the bifurcations of SSR is also investigated. The results obtained on replacing the fixed series compensation of the line by Static Synchronous Series Compensator resulted in the mitigation of Sub-synchronous Resonance. The results obtained for all the above-considered cases are compared with eigenvalue analysis and validated using transient analysis<strong>.</strong>

Bifurcation Mechanism of Carbon Nanotubes and its Application Prospects

This article outlines the various processes for CNT growth. The surface morphology of carbon nanotubes on carbon nanotubes was characterized by scanning electron microscopy (TEM) and transmission electron microscopy (TEM). Bifurcated carbon nanotubes were founded. Mechanism analysis was studied of bifurcated carbon nanotubes from chemical crystallization bifurcation and nonlinear dynamic bifurcation. At present, 5nm or 7nm chip fabrication is limited by quantum effects, which makes Moore's Law invalid. Bifurcated carbon nanotubes may be the development direction of new transistors.